{"paper":{"title":"The algebra of integro-differential operators on an affine line and its modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2010-11-12T18:08:33Z","abstract_excerpt":"For the algebra $\\mI_1= K<x, \\frac{d}{dx}, \\int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\\mI_1$ is a left and right coherent algebra. The {\\em Strong Compact-Fredholm Alternative} is proved for $\\mI_1$. The endomorphism algebra of each simple $\\mI_1$-module is a {\\em finite dimensional} skew field. In contrast to the first Weyl algebra, the centralizer of a non-scalar integro-differential operator can be a noncommutative, non-Noetherian, non-finitely generated algebra which is not a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2997","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}